Abstract
The propagation of non-topological solitons in many-nucleus systems is studied based on timedependent density functional calculations, focusing on mass and energy dependence. The dispersive property and the nonlinearity of the system, which are inherently included in the nuclear density functional, are essential factors to form a non-topological soliton. On the other hand, soliton propagation is prevented by charge equilibration, and competition can appear between soliton formation and disruption. In this article, based on the energy-dependence of the two competitive factors, the concept of conditional recovery of time-reversal symmetry is proposed in many-nucleus systems. It clarifies the possibility of preserving the nuclear medium inside natural or artificial nuclear reactors, at a suitable temperature. From an astrophysical point of view, the existence of the low-temperature solitonic core of compact stars is suggested.